mathematics

Neil Trudinger

Neil Trudinger is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Neil Trudinger rather than just read about it. In short: Neil Sidney Trudinger (born 20 June 1942) is an Australian mathematician, known particularly for his work in the field of nonlinear elliptic partial differential equations. After completing his BSc at the University of New England (Australia) in 1962, he continued his graduate studies at Stanford University.

Key takeaways

Neil Trudinger belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Neil Trudinger to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Neil Trudinger from memory before moving on to harder problems.

Reference excerpt

Neil Sidney Trudinger (born 20 June 1942) is an Australian mathematician, known particularly for his work in the field of nonlinear elliptic partial differential equations. After completing his BSc at the University of New England (Australia) in 1962, he continued his graduate studies at Stanford University. He was awarded a PhD in 1966 for his thesis Quasilinear Elliptical Partial Differential Equations in n Variables. After the award of his doctorate from Stanford University, Trudinger became a Courant Instructor at the Courant Institute of Mathematical Sciences of New York University during the academic year 1966–67. He then returned to Australia, where he was appointed as a lecturer at Macquarie University in 1967. In 1970, he moved to University of Queensland, where he was first appointed as a reader, then as professor. In 1973 he moved to the Australian National University. In 2016 he moved to the University of Wollongong, where he is currently appointed as a distinguished professor. At the ANU Trudinger served as head of the Department of Pure Mathematics, as director of the Centre for Mathematical Analysis and as director of the Centre for Mathematics and its Applications, before becoming dean of the School of Mathematical Sciences in 1992. He is co-author, together with his thesis advisor, David Gilbarg, of the book Elliptic Partial Differential Equations of Second Order.

Honours 1978, elected as a fellow of the Australian Academy of Science. 1981, first recipient of the Australian Mathematical Society Medal. 1996, awarded the Hannan Medal of the Australian Academy of Science. 1997, elected as a Fellow of the Royal Society of London. 2008, awarded the Leroy P. Steele Prize for Mathematical Exposition by the American Mathematical Society. 2012, elected as a fellow of the American Mathematical Society. 2014, gave the Łojasiewicz Lecture (on the "Optimal Transportation in the 21st Century") at the Jagiellonian University in Kraków.

See also Trudinger's theorem Yamabe problem

References

Illustrations

Worked examples

Example 1 — a first encounter with Neil Trudinger

Start with the simplest possible case. Write down what Neil Trudinger claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Neil Trudinger before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Neil Trudinger ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Neil Trudinger

In research: Neil Trudinger appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Neil Trudinger in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Neil Trudinger is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1942 births, 20th-century Australian mathematicians, 21st-century Australian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Neil Trudinger outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Neil Trudinger in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Neil Trudinger means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Neil Trudinger out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Neil Trudinger in simple terms?

Why does Neil Trudinger matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Neil Trudinger?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Neil Trudinger.